15 citations · 38 across the 11 of their papers we have counts for
21 papers
Discontinuous Galerkin schemes for multi-dimensional coupled hyperbolic systems
Niklas Kolbe, Siegfried Müller, Aleksey Sikstel
A novel class of Runge-Kutta discontinuous Galerkin schemes for coupled systems of conservation laws in multiple space dimensions that are separated by a fixed sharp interface is i…
A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid
Niklas Kolbe, Siegfried Müller
A recently developed coupling strategy for two nonconservative hyperbolic systems is employed to investigate a collapsing vapor bubble embedded in a liquid near a solid. For this p…
A one-dimensional model for aspiration in blood vessels
Niklas Kolbe, Dimitrios Katsaounis, Xiangge Yin +1
This work introduces a reduced one-dimensional model for aspiration in blood vessels that accounts for the elasticity of both the vessel wall and the catheter. The inclusion of ves…
Numerical schemes for coupled systems of nonconservative hyperbolic equations
Niklas Kolbe, Michael Herty, Siegfried Müller
A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system…
A data-driven microscopic on-ramp model based on macroscopic network flows
Niklas Kolbe, Moritz Berghaus, Eszter Kalló +2
While macroscopic traffic flow models consider traffic as a fluid, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic pheno…
A central scheme for coupled hyperbolic systems
Michael Herty, Niklas Kolbe, Siegfried Müller
A novel numerical scheme to solve coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the L…
Data-Driven Models for Traffic Flow at Junctions
Michael Herty, Niklas Kolbe
The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist…
Numerical relaxation limit and outgoing edges in a central scheme for networked conservation laws
Niklas Kolbe
A recently introduced scheme for networked conservation laws is analyzed in various experiments. The scheme makes use of a novel relaxation approach that governs the coupling condi…
Central schemes for networked scalar conservation laws
Michael Herty, Niklas Kolbe, Siegfried Müller
We propose a novel scheme to numerically solve scalar conservation laws on networks without the necessity to solve Riemann problems at the junction. The scheme is derived using the…
Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF- signaling
Niklas Kolbe, Lorenz Hexemer, Lukas-Malte Bammert +3
Cells sense their surrounding by employing intracellular signaling pathways that transmit hormonal signals from the cell membrane to the nucleus. TGF-/SMAD signaling encodes var…
A mass-preserving two-step Lagrange-Galerkin scheme for convection-diffusion problems
Kouta Futai, Niklas Kolbe, Hirofumi Notsu +1
A mass-preserving two-step Lagrange-Galerkin scheme of second order in time for convection-diffusion problems is presented, and convergence with optimal error estimates is proved i…
Multiscale modeling of glioma invasion: from receptor binding to flux-limited macroscopic PDEs
Anne Dietrich, Niklas Kolbe, Nikolaos Sfakianakis +1
We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasi…
Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence
Niklas Kolbe, Nikolaos Sfakianakis, Christian Stinner +2
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually…
A hybrid mass transport finite element method for Keller-Segel type systems
José Antonio Carrillo, Niklas Kolbe, Mária Lukácová-Medviďová
We propose a new splitting scheme for general reaction-taxis-diffusion systems in one spatial dimension capable to deal with simultaneous concentrated and diffusive regions as well…
An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models
Niklas Kolbe, Nikolaos Sfakianakis
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2-…
Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model
Jan Giesselmann, Niklas Kolbe, Maria Lukacova-Medvidova +1
We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model de…
Chemotaxis and Haptotaxis on Cellular Level
Aaron Brunk, Niklas Kolbe, Nikolaos Sfakianakis
Chemotaxis and haptotaxis have been a main theme in the macroscopic study of bacterial and cellular motility. In this work we investigate the influence these processes have on the…
Numerical simulation of a contractivity based multiscale cancer invasion model
Niklas Kolbe, Maria Lukacova-Medvidova, Nikolaos Sfakianakis +1
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that de…
A multiscale approach to the migration of cancer stem cells: mathematical modelling and simulations
Nikolaos Sfakianakis, Niklas Kolbe, Nadja Hellmann +1
We propose a multiscale model of the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We assume that th…
A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix
Nadja Hellmann, Niklas Kolbe, Nikolaos Sfakianakis
Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are term…
Numerical study of cancer cell invasion dynamics using adaptive mesh refinement: the urokinase model
Niklas Kolbe, Jana Katuchova, Nikolaos Sfakianakis +2
In the present work we investigate the chemotactically and proteolytically driven tissue invasion by cancer cells. The model employed is a system of advection-reaction-diffusion eq…